The paper shows the unique solvability of the classical Dirichlet problem in cylindrical domain for threedimensional elliptic equations with degeneration of type and order.
References
A. V. Bitsadze, Equations of Mixed Type [in Russian], Akad. Nauk SSSR, Moscow (1959).
A. V. Bitsadze, Boundary-Value Problems for Elliptic Equations of the Second Order [in Russian], Nauka, Moscow (1966).
A. V. Bitsadze, Some Classes of Partial Differential Equations [in Russian], Nauka, Moscow (1981).
S. A. Aldashev, “Well-posedness of the Dirichlet problem in a cylindrical domain for the degenerate three-dimensional elliptic equation,” in: Proc. of the Seventh Lyashko Internat. Sci. Conf. (2014), pp. 14–15.
L. Bers, F. John, and M. Schechter, Partial Differential Equations, Interscience Publ., New York (1964).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1976).
S. A. Aldashev, “Well-posedness of the Dirichlet problem in a cylindrical domain for the degenerate multidimensional elliptic equations,” Mat. Zametki, 94, Issue 6, 936–939 (2013).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 9, pp. 1270–1274, September, 2017.
Rights and permissions
About this article
Cite this article
Aldashev, S.A., Kitaibekov, E.T. Well-Posedness of the Dirichlet Problem in a Cylindrical Domain for Three-Dimensional Elliptic Equations with Degeneration of Type and Order. Ukr Math J 69, 1473–1478 (2018). https://doi.org/10.1007/s11253-018-1446-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-018-1446-7